Solve for $z$, $ \dfrac{4}{4z + 20} = -\dfrac{z - 10}{z + 5} - \dfrac{8}{2z + 10} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $4z + 20$ $z + 5$ and $2z + 10$ The common denominator is $4z + 20$ The denominator of the first term is already $4z + 20$ , so we don't need to change it. To get $4z + 20$ in the denominator of the second term, multiply it by $\frac{4}{4}$ $ -\dfrac{z - 10}{z + 5} \times \dfrac{4}{4} = -\dfrac{4z - 40}{4z + 20} $ To get $4z + 20$ in the denominator of the third term, multiply it by $\frac{2}{2}$ $ -\dfrac{8}{2z + 10} \times \dfrac{2}{2} = -\dfrac{16}{4z + 20} $ This give us: $ \dfrac{4}{4z + 20} = -\dfrac{4z - 40}{4z + 20} - \dfrac{16}{4z + 20} $ If we multiply both sides of the equation by $4z + 20$ , we get: $ 4 = -4z + 40 - 16$ $ 4 = -4z + 24$ $ -20 = -4z $ $ z = 5$